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Simplifying x2 + 3.2x + -9 = 0 Reorder the terms: -9 + 3.2x + x2 = 0 Solving -9 + 3.2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 3.2x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 3.2x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 3.2x + x2 = 0 + 9 3.2x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 3.2x + x2 = 9 The x term is 3.2x. Take half its coefficient (1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. 3.2x + 2.56 + x2 = 9 + 2.56 Reorder the terms: 2.56 + 3.2x + x2 = 9 + 2.56 Combine like terms: 9 + 2.56 = 11.56 2.56 + 3.2x + x2 = 11.56 Factor a perfect square on the left side: (x + 1.6)(x + 1.6) = 11.56 Calculate the square root of the right side: 3.4 Break this problem into two subproblems by setting (x + 1.6) equal to 3.4 and -3.4.Subproblem 1
x + 1.6 = 3.4 Simplifying x + 1.6 = 3.4 Reorder the terms: 1.6 + x = 3.4 Solving 1.6 + x = 3.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = 3.4 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 3.4 + -1.6 x = 3.4 + -1.6 Combine like terms: 3.4 + -1.6 = 1.8 x = 1.8 Simplifying x = 1.8Subproblem 2
x + 1.6 = -3.4 Simplifying x + 1.6 = -3.4 Reorder the terms: 1.6 + x = -3.4 Solving 1.6 + x = -3.4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = -3.4 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -3.4 + -1.6 x = -3.4 + -1.6 Combine like terms: -3.4 + -1.6 = -5 x = -5 Simplifying x = -5Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8, -5}
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